Floating Phase in 1D Transverse ANNNI Model

Abstract

To study the ground state of ANNNI chain under transverse field as a function of frustration parameter $\kappa$ and field strength $\Gamma$, we present here two different perturbative analyses. In one, we consider the (known) ground state at $\kappa =0.5$ and $\Gamma =0$ as the unperturbed state and treat an increase of the field from 0 to $\Gamma$ coupled with an increase of $\kappa$ from 0.5 to $0.5+r\Gamma$ as perturbation. The first order perturbation correction to eigenvalue can be calculated exactly and we could conclude that there are only two phase transition lines emanating from the point $\kappa =0.5$, $\Gamma =0$. In the second perturbation scheme, we consider the number of domains of length 1 as the perturbation and obtain the zero-th order eigenfunction for the perturbed ground state. From the longitudinal spin-spin correlation, we conclude that floating phase exists for small values of transverse field over the entire region intermediate between the ferromagnetic phase and antiphase.

11 pages, 11 figures

References in corpus (3)

• Gapless line for the anisotropic Heisenberg spin-1/2 chain in a magnetic field and the quantum axial next-nearest-neighbor Ising Chain
• Infinitesimal incommensurate stripe phase in an axial next-nearest-neighbor Ising model in two dimensions
• The One-Dimensional ANNNI model in a Transverse Field: Analytic and numerical study of Effective Hamiltonians

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